On the saturation of subfields of invariants of finite groups

Abstract

Every subfield \(
\mathbb{K}
\)(φ) of the field of rational fractions \(
\mathbb{K}
\)(x1,..., xn) is contained in a unique maximal subfield of the form \(
\mathbb{K}
\)(ω). The element ω is said to be generating for the element φ. A subfield of \(
\mathbb{K}
\)(x1,..., xn) is said to be saturated if, together with every its element, the subfield also contains the generating element. In the paper, the saturation property is studied for the subfields of invariants \(
\mathbb{K}
\)(x1,..., xn)G of a finite group G of automorphisms of the field \(
\mathbb{K}
\)(x1..., xn).